This thesis looks at entertainment bias, specifically bias on the Tonight Show with Jay Leno towards Arnold Schwarzenegger during the time leading up to the California recall election in 2003. Entertainment media possess a unique ability to communicate messages to an unguarded audience, which gives them the potential to have more of a political impact than traditional news media. The basic theory is that Jay Leno showed political bias in his monologues towards his friend and gubernatorial candidate, Arnold Schwarzenegger. This theory was tested through a highly detailed descriptive analysis of monologue jokes and summary data for the time period March 31, 2003 to October 6, 2003. In total, there were 388 jokes from monologues of the Tonight Show analyzed. These jokes were broken down into categories based on their content and the subject. They were then compared to jokes delivered on the Late Show with David Letterman about the California recall election. The analysis of jokes showed that the manner in which candidates were portrayed on the Tonight Show with Jay Leno was politically biased towards Arnold Schwarzenegger. Due to the differences in program structure it was difficult to determine if this political bias was also present in the Late Show with David Letterman. / Master of Arts

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[EN] The concept of progressive variation refers to a creative process that was first raised by Arnold Schoenberg, focusing mainly on the music of Brahms. This thesis investigates the role such proceedings have in Verklärte Nacht, Schoenberg's earliest masterwork, exploring till what extent they rule the relationships between all the themes appearing in the piece. The first part sets the basis of this study in five chapters dedicated, respectively, to the presence of cadences, importance of the sequences, remarkable harmonic issues, overall structure of the work and an essay on the concept of progressive variation that serves as an introduction to the thematic analysis that follows. The second part is devoted to a systematic analysis of the motives appearing in Verklärte Nacht, which leads to the conclusion that all of them are originated on a basic form or Gestalt . Given the weak presence of cadential processes, the limited functionality of harmony and the apparently inconsistent formal structure of the work, the thematic analysis of the piece brings out the progressive variation as an essential element of cohesion and unity. The widespread use of motivic development as a way of creating music gives great independence to the voices and many harmonics events begin to be casual rather than causal. The qualities of the processes explored and described in this study lead to the conclusion that motivic development can be considered the link between tonal and atonal music, since it is a common procedure on both sides. Therefore, it can be suggested that Schoenberg's path towards atonality was not a sudden change or a break, but a continuous evolution that finds its main thread in the method of motivic construction. / [ES] El concepto de variación progresiva se refiere a un procedimiento creativo que fue planteado por primera vez por Arnold Schoenberg centrándose, sobre todo, en la música de Brahms. Esta tesis investiga el papel que dicho procedimiento tiene en Verklärte Nacht, la primera obra maestra de Schoenberg, explorando hasta qué punto marca las relaciones entre todos los temas que aparecen en ella. La primera parte sienta las bases del estudio en cinco capítulos dedicados, respectivamente, a la presencia de cadencias, la importancia de las secuencias, los elementos armónicos destacables, la estructura general de la obra y un ensayo sobre el concepto mismo de la variación progresiva como introducción al análisis temático que le sigue. La segunda parte efectúa el análisis sistemático de los motivos que aparecen en Verklärte Nacht, el cual lleva a la conclusión de que todos ellos provienen de una forma básica o Gestalt. Dada la débil presencia de procesos cadenciales, la escasa funcionalidad de la armonía y la poco cohesionada estructura formal de la obra, el análisis temático de la pieza descubre en la variación progresiva el elemento primordial de cohesión y unidad. La generalización del uso del desarrollo motívico como forma de crear música otorga a las voces una gran independencia y muchos sucesos armónicos comienzan a ser casuales, en vez de causales. Las cualidades de los procesos explorados y descritos durante este estudio llevan a la conclusión de que el desarrollo motívico se puede considerar el nexo de unión entre la música tonal y la atonal, ya que es un procedimiento común en ambos bandos, con lo cual se puede decir que el camino de Schoenberg hacia la atonalidad no fue un cambio brusco ni una ruptura, sino una evolución continua que encuentra su principal hilo conductor en el proceso de construcción motívica. / [CA] El concepte de variació progressiva es referix a un procediment creatiu que va ser plantejat per primera vegada per Arnold Schoenberg centrant-se, sobretot, en la música de Brahms. Esta tesi investiga el paper que el dit procediment té en Verklärte Nacht, la primera Schoenberg primerenc, explorant fins a quin punt marca les relacions entre tots els temes que apareixen en ella. La primera part assenta les bases de l'estudi en cinc capítols dedicats, respectivament, a la presència de cadències, la importància de les seqüències, els elements harmònics destacables, l'estructura general de l'obra i un assaig sobre el concepte mateix de la variació progressiva com a introducció a l'anàlisi temàtica que li seguix. La segona part efectua l'anàlisi sistemàtica dels motius que apareixen en Verklärte Nacht, el qual porta a la conclusió que tots ells provenen d'una forma bàsica o Gestalt. Donada la dèbil presència de processos cadenciales, l'escassa funcionalitat de l'harmonia i la poc cohesionada estructura formal de l'obra, l'anàlisi temàtica de la peça descobrix en la variació progressiva l'element primordial de cohesió i unitat. La generalització de l'ús del desenrotllament motívic com a forma de crear música atorga a les veus una gran independència i molts esdeveniments harmònics comencen a ser casuals, en compte de causals. Les qualitats desl processos explorats i descrits durant este estudi porten a la conclusió que el desenrotllament motívic es pot considerar el nexe d'unió entre la música tonal i l'atonal, ja que és un procediment comú en ambdós camps, amb la qual cosa es pot dir que el camí de Schoenberg cap a l'atonalitat no va ser un canvi brusc ni una ruptura, sinó una evolució contínua que troba el seu principal fil conductor en el mètode de la construcció motívica. / Amat Arocas, C. (2016). La variación progresiva en Verklärte Nacht, op. 4, de Arnold Schoenberg y su importancia en la construcción de la obra, así como en la evolución de su método de escritura [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/62823

Québec Université Laval, Bibliothèque 2014

Thesis advisor: Elisa Magri / This thesis will argue that art expresses feeling, affirming the expressivist theory of aesthetics of R.G. Collingwood, and will expand this thesis to say that aesthetic experience of nature is also expressive. By aesthetic experience of nature, I refer to an experience in which the subject is not merely observing, but appreciating the natural world for its aesthetic qualities. I will present the argument that such experiences of nature are governed by the same principles of expression and imagination that intentionally made art objects are. I will begin with an analysis of the expressivist theory of Collingwood, which asserts that all proper art is the result of expression followed by an act of imaginative creation. Following this, I will investigate the expression of feelings in the non-art aesthetic experience of nature. To do this I will present the work of Arnold Berleant, whose framework for aesthetic engagement will allow the expressivist theory of expression and imagination to apply in natural aesthetics. With this framework in place I will explore several examples of aesthetic experience of nature to illustrate this process at work. / Thesis (BA) — Boston College, 2024. / Submitted to: Boston College. Morrissey School of Arts and Sciences. / Discipline: Philosophy. / Discipline: Departmental Honors.

[pt] O objetivo desta pesquisa é estudar as propriedades geométricas e topológicas de curvas genéricas imersas no plano. Neste caso ser genérica significa que a curva só pode ter pontos duplos sem tangentes comuns nas duas passagens. Pode-se nomear as n singularidades da curva usando símbolos como a1, ... , an. Percorrendo a curva, produz-se uma palavra cíclica de tamanho 2n. Entretanto, nem toda palavra está relacionada a uma curva plana, há requisitos sobre a sua combinatória, o primeiro dos quais foi descoberto por Gauss. Avanços foram realizados no estudo de curvas localmente convexas no plano, na esfera e no plano projetivo. / [en] The aim of this work is to study the topological and geometric properties of closed generic immersed curves in the plane. In this case, generic means that the curve can only have double points without a common tangent. One can label the singularities using n symbols, such as a1, ... , an. Going around the curve, a cyclic word of length 2n is produced. However, not every word is related to a planar curve, there are requirements on its combinatorics, the first of which was found by Gauss. Advances were made in the study of locally convex curves on the plane, the sphere and the projective plane.

Für das Verständnis einer Vielzahl von Problemen von der Himmelsmechanik bis hin zur Beschreibung von Molekülen spielen Systeme mit mehr als zwei Freiheitsgraden eine entscheidende Rolle. Aufgrund der Dimensionalität gestaltet sich ein Verständnis dieser Systeme jedoch deutlich schwieriger als bei Systemen mit zwei oder weniger Freiheitsgraden. Die vorliegende Arbeit soll zum besseren Verständnis der klassischen und quantenmechanischen Eigenschaften getriebener Systeme mit zwei Freiheitsgraden beitragen. Hierzu werden dreidimensionale Schnitte durch den Phasenraum von 4D Abbildungen betrachtet. Anhand dreier Beispiele, deren Phasenräume zunehmend kompliziert sind, werden diese 3D Schnitte vorgestellt und untersucht. In einer sich anschließenden quantenmechanischen Untersuchung gehen wir auf zwei wichtige Aspekte ein. Zum einen untersuchen wir die quantenmechanischen Signaturen des klassischen "Arnold Webs". Es wird darauf eingegangen, wie die Quantenmechanik dieses Netz im semiklassischen Limes auflösen kann. Darüberhinaus widmen wir uns dem wichtigen Aspekt quantenmechanischer Kopplungen klassisch getrennter Phasenraumgebiete anhand der Untersuchung dynamischer Tunnelraten. Für diese wenden wir sowohl den in der Literatur bekannten "fictitious integrable system approach" als auch die Theorie des resonanz-unterstützen Tunnelns auf 4D Abbildungen an.:Contents ..... v 1 Introduction ..... 1 2 2D mappings ..... 5 2.1 Hamiltonian systems with 1.5 degrees of freedom ..... 5 2.2 The 2D standard map ..... 6 3 Classical dynamics of higher dimensional systems ..... 11 3.1 Coupled standard maps as paradigmatic example ..... 12 Stability of fixed points in 4D maps ..... 13 Center manifolds of elliptic degrees of freedom ..... 13 3.2 Near-integrable systems ..... 15 3.2.1 Analytical description of multidimensional, near-integrable systems ..... 15 Resonance structures in 4D maps ..... 16 3.2.2 Pendulum approximation ..... 18 3.2.3 Normal forms ..... 24 3.2.4 Arnold diffusion and Arnold web ..... 24 3.3 Numerical tools for the analysis of regular and chaotic motion ..... 26 3.3.1 Frequency analysis ..... 26 Aim of the frequency analysis ..... 26 Realizations of the frequency analysis ..... 27 Wavelet transforms ..... 30 3.3.2 Fast Lyapunov indicator ..... 31 3.3.3 Phase-space sections ..... 33 Skew phase-space sections containing invariant eigenspaces ..... 34 3.4 Systems with regular dynamics and a large chaotic sea ..... 35 3.4.1 Designed maps: Map with linear regular region, P_llu ..... 36 Phase space of the designed map with linear regular region ..... 38 FLI values ..... 41 Estimating the size of the regular region ..... 43 3.4.2 Designed maps: Islands with resonances, P_nnc ..... 46 Frequency analysis ..... 46 FLI values and volume of the regular and stochastic region ..... 50 Frequency analysis for rank-2 resonance ..... 52 Phase-space sections at different positions p_1 and p_2 ..... 53 Using color to provide the 4-th coordinate ..... 53 Skew phase-space sections containing invariant eigenspaces ..... 57 Arnold diffusion ..... 58 3.4.3 Generic maps: Coupled standard maps, P_csm ..... 63 FLI values and volume of the regular and stochastic region ..... 63 Analysis of fundamental frequencies ..... 66 Skew phase-space sections containing invariant eigenspaces ..... 69 4 Quantum Mechanics ..... 75 4.1 Quantization of Classical Maps ..... 77 4.2 Eigenstates of the time evolution operator U ..... 79 4.2.1 Eigenstates of P_llu ..... 80 4.2.2 Eigenstates of P_nnc ..... 84 4.2.3 Eigenstates of P_csm ..... 87 4.3 Quantum signatures of the stochastic layer ..... 89 4.3.1 Eigenstates resolving the stochastic layer ..... 90 4.3.2 Wave-packet dynamics into the stochastic layer ..... 94 4.4 Dynamical tunneling rates ..... 98 4.4.1 Numerical calculation of dynamical tunneling rates ..... 99 4.4.2 Direct regular-to-chaotic tunneling rates gamma^d of P_llu ..... 101 4.4.3 Prediction of gamma^d using the fictitious integrable system approach ..... 103 4.4.4 Dynamical tunneling rates of P_nnc ..... 105 4.4.5 Interlude: Theory of resonance assisted tunneling (RAT) ..... 106 4.4.6 Prediction of tunneling rates for P_nnc, RAT ..... 111 Selection rules from nonlinear resonances ..... 111 Energy denominators ..... 114 Estimating the parameters of the pendulum approximation from phase-space properties ..... 116 Prediction ..... 118 4.4.7 Dynamical tunneling rates of P_csm ..... 120 5 Summary and outlook ..... 123 Appendix ..... 125 A Potential of the designed map ..... 125 B Quantum-number assignment-algorithm ..... 128 C Alternate paths due to alternate resonances in the description of RAT ..... 131 D Alternate resonances in the description of RAT leading to different tunneling rates ..... 133 E Tunneling rates of map with nonlinear resonances but uncoupled regular region ..... 133 F Interpolation of quasienergies ..... 135 G 2D Poincar'e map for the pendulum approximation ..... 137 H RAT prediction broken down to single paths ..... 139 I Linearization of the pendulum approximation ..... 140 J Iterative diagonalization schemes for the semiclassical limit ..... 143 Inverse iteration ..... 143 Arnoldi method ..... 144 Lanczos algorithm ..... 144 List of figures ..... 148 Bibliography ..... 163 / Systems with more than two degrees of freedom are of fundamental importance for the understanding of problems ranging from celestial mechanics to molecules. Due to the dimensionality the classical phase-space structure of such systems is more difficult to understand than for systems with two or fewer degrees of freedom. This thesis aims for a better insight into the classical as well as the quantum mechanics of 4D mappings representing driven systems with two degrees of freedom. In order to analyze such systems, we introduce 3D sections through the 4D phase space which reveal the regular and chaotic structures. We introduce these concepts by means of three example mappings of increasing complexity. After a classical analysis the systems are investigated quantum mechanically. We focus especially on two important aspects: First, we address quantum mechanical consequences of the classical Arnold web and demonstrate how quantum mechanics can resolve this web in the semiclassical limit. Second, we investigate the quantum mechanical tunneling couplings between regular and chaotic regions in phase space. We determine regular-to-chaotic tunneling rates numerically and extend the fictitious integrable system approach to higher dimensions for their prediction. Finally, we study resonance-assisted tunneling in 4D maps.:Contents ..... v 1 Introduction ..... 1 2 2D mappings ..... 5 2.1 Hamiltonian systems with 1.5 degrees of freedom ..... 5 2.2 The 2D standard map ..... 6 3 Classical dynamics of higher dimensional systems ..... 11 3.1 Coupled standard maps as paradigmatic example ..... 12 Stability of fixed points in 4D maps ..... 13 Center manifolds of elliptic degrees of freedom ..... 13 3.2 Near-integrable systems ..... 15 3.2.1 Analytical description of multidimensional, near-integrable systems ..... 15 Resonance structures in 4D maps ..... 16 3.2.2 Pendulum approximation ..... 18 3.2.3 Normal forms ..... 24 3.2.4 Arnold diffusion and Arnold web ..... 24 3.3 Numerical tools for the analysis of regular and chaotic motion ..... 26 3.3.1 Frequency analysis ..... 26 Aim of the frequency analysis ..... 26 Realizations of the frequency analysis ..... 27 Wavelet transforms ..... 30 3.3.2 Fast Lyapunov indicator ..... 31 3.3.3 Phase-space sections ..... 33 Skew phase-space sections containing invariant eigenspaces ..... 34 3.4 Systems with regular dynamics and a large chaotic sea ..... 35 3.4.1 Designed maps: Map with linear regular region, P_llu ..... 36 Phase space of the designed map with linear regular region ..... 38 FLI values ..... 41 Estimating the size of the regular region ..... 43 3.4.2 Designed maps: Islands with resonances, P_nnc ..... 46 Frequency analysis ..... 46 FLI values and volume of the regular and stochastic region ..... 50 Frequency analysis for rank-2 resonance ..... 52 Phase-space sections at different positions p_1 and p_2 ..... 53 Using color to provide the 4-th coordinate ..... 53 Skew phase-space sections containing invariant eigenspaces ..... 57 Arnold diffusion ..... 58 3.4.3 Generic maps: Coupled standard maps, P_csm ..... 63 FLI values and volume of the regular and stochastic region ..... 63 Analysis of fundamental frequencies ..... 66 Skew phase-space sections containing invariant eigenspaces ..... 69 4 Quantum Mechanics ..... 75 4.1 Quantization of Classical Maps ..... 77 4.2 Eigenstates of the time evolution operator U ..... 79 4.2.1 Eigenstates of P_llu ..... 80 4.2.2 Eigenstates of P_nnc ..... 84 4.2.3 Eigenstates of P_csm ..... 87 4.3 Quantum signatures of the stochastic layer ..... 89 4.3.1 Eigenstates resolving the stochastic layer ..... 90 4.3.2 Wave-packet dynamics into the stochastic layer ..... 94 4.4 Dynamical tunneling rates ..... 98 4.4.1 Numerical calculation of dynamical tunneling rates ..... 99 4.4.2 Direct regular-to-chaotic tunneling rates gamma^d of P_llu ..... 101 4.4.3 Prediction of gamma^d using the fictitious integrable system approach ..... 103 4.4.4 Dynamical tunneling rates of P_nnc ..... 105 4.4.5 Interlude: Theory of resonance assisted tunneling (RAT) ..... 106 4.4.6 Prediction of tunneling rates for P_nnc, RAT ..... 111 Selection rules from nonlinear resonances ..... 111 Energy denominators ..... 114 Estimating the parameters of the pendulum approximation from phase-space properties ..... 116 Prediction ..... 118 4.4.7 Dynamical tunneling rates of P_csm ..... 120 5 Summary and outlook ..... 123 Appendix ..... 125 A Potential of the designed map ..... 125 B Quantum-number assignment-algorithm ..... 128 C Alternate paths due to alternate resonances in the description of RAT ..... 131 D Alternate resonances in the description of RAT leading to different tunneling rates ..... 133 E Tunneling rates of map with nonlinear resonances but uncoupled regular region ..... 133 F Interpolation of quasienergies ..... 135 G 2D Poincar'e map for the pendulum approximation ..... 137 H RAT prediction broken down to single paths ..... 139 I Linearization of the pendulum approximation ..... 140 J Iterative diagonalization schemes for the semiclassical limit ..... 143 Inverse iteration ..... 143 Arnoldi method ..... 144 Lanczos algorithm ..... 144 List of figures ..... 148 Bibliography ..... 163

Arnold Schoenberg's String Quartet No. 1, Op. 7 stands out as being the first chamber music piece to use a vast number and variety of extended string techniques within one composition. This paper examines a brief history of extended string techniques in chamber music, analyses the unique ways in which Schoenberg applied extended string techniques to manipulate motives in his Op. 7 quartet, and ultimately shows that Schoenberg's use of extended string techniques influenced future composers to employ even more extended techniques and special effects in their own twentieth-century chamber music.

Cette thèse se propose de démontrer que, au-delà de son image d’interprète de la musique de Jean-Sébastien Bach, le pianiste Glenn Gould a développé, à travers ses nombreux écrits, une véritable pensée musicologique, qui surprend par sa cohérence et dont les racines sont à chercher en réalité du côté d’Arnold Schoenberg, le compositeur qui l’aura le plus influencé. Nous nous attachons donc ici à l’observation et à l’analyse de cette pensée à travers les écrits du musicien canadien, l’objectif étant la mise en évidence du rapport existant avec la pensée de Schoenberg. L’analyse comparative menée ici repose sur les principes que Gould avait lui-même placés au fondement de sa pensée : le raisonnement justifiable, l’esprit de re-création, le concept inductif et la musicologie scientifique. Pour ce faire, nous avons adopté un cheminement logique passant successivement par les domaines suivants : méthode, création musicale, interprétation, critique, pédagogie et enregistrement. / This research tends to demonstrate that, beyond the picture of the performer of Johann Sebastian Bach’s music, Glenn Gould, the pianist, has developed through his numerous writings a real musicological thought which is distinguished by a strong coherence ; its roots are in fact to be found in Arnold Schoenberg’s thought, the composer whose influence was the most important for Gould. We intend here to propose an analytical and critical observation of Glenn Gould’s musicological thought by using the principles upon which he had himself set his thought, which are : justified reasoning, re-creation spirit, inductive concept and scientific musicology. With that aim, we used a logical progression examining successively the following themes : the method, the musical creation, the musical performance, the criticism, the pedagogy and finally the recording.